Martensite Crystallography Research Articles

PTCLab: free and open-source software for calculating phase transformation crystallography

PTCLab(Phase Transformation Crystallography Lab) is free and open-source software to calculate the crystallographic features formed during a phase transformation, such as orientation relationship, interface orientation, interfacial structureetc. This program covers the crystallographic theories for both martensitic and diffusional transformation and allows users to represent the results in stereographic projection. The crystallographic models treated inPTCLabinclude the classical phenomenological theory of martensite crystallography (PTMC), the double shear version of PTMC, the invariant line model, O-lattice theory, the O-line model, the recently developed three-dimensional near coincidence site method, the edge-to-edge matching model and variant selection analysis. In addition, a number of basic crystallographic calculations for single or multiple crystal structures can be performed with the calculation pad. High-quality composite stereographic projection and electron diffraction patterns can be also obtained by the present application.PTCLabis written in Python, runnable cross platform, and is distributed at https://sourceforge.net/projects/tclab/.

Effect of Solution Carbon and Nitrogen on the Microstructural Size and Crystallography of Lath Martensite in Fe–N and Fe–C Alloys

Microstructures of lath martensite that contains bcc or bct martensite crystals in Fe–C alloys are known to depend on the carbon content of the alloys. The effect of nitrogen content on microstructure, however, has not yet been elucidated. This study elucidates the effects of carbon and nitrogen content on microstructures via local crystallographic analysis. We found that the packet sizes are similar when the nitrogen content in the alloys are the same as the carbon content, with the packet size decreasing with increasing carbon and nitrogen content. The block and sub-block thicknesses in low nitrogen lath martensite are smaller than those in low carbon lath martensite, whereas those in medium and high carbon and nitrogen lath martensites are similar. Martensite lath thickness and dislocation density in the Fe–N alloy laths are lower than those in the Fe–C alloys laths, and the distribution of misorientation angles between adjacent the blocks and sub-blocks in Fe–N alloys is similar to that in Fe–C alloys.

Crystallographic analysis of lenticular martensite in Fe–1.0C–17Cr stainless steel by electron backscatter diffraction

The crystallography of lenticular martensite, which formed in coarse austenite grains (size about 80μm) after subzero treatment at −196°C (liquid nitrogen) for different holding times, was investigated using electron backscatter diffraction (EBSD). For the sample treated with 15min of isothermal holding, more than 50 martensite plates (with a thickness of larger than 1μm) that formed within a coarse austenite grain were employed to obtain the pole figures. The pole figures clearly indicated that the individual plate of lenticular martensite approximately adopted the Kurdjumov–Sachs (K–S) orientation relationship with respect to the austenite matrix. For the sample treated with 30s of isothermal holding, a few martensite plates that formed in variant pairings in a coarse austenite grain were analyzed. The results showed that zigzag couplings (including spear couplings), the major product of plate martensite, had an absolute dominance of a specific variant pair (V1/V17). The orientation gradient within a lenticular martensite plate was also measured using convergent beam electron diffraction (CBED). The evidence strongly suggests that the spread in diffracted intensity within pole figures is related to the misorientation gradient within the lenticular martensite plate.

Crystallographic variant selection of martensite at high stress/strain

The phenomenological theory of martensitic transformation is well understood that the displacive phase transformations are mainly influenced by the externally applied stress. Martensitic transformation occurs with 24 possible Kurdjomov-Sachs (K-S) variants, where each variant shows a distinct lattice orientation. The elegant transformation texture model of Kundu and Bhadeshia for crystallographic variant selection of martensite in metastable austenite at various stress/strain levels has been assessed in this present research. The corresponding interaction energies have also been evaluated. Encouraging correlation between model prediction and experimental data generation for martensite pole figures at many deformed austenite grains has been observed at different stress/strain levels. It has been investigated that the mechanical driving force alone is able to explain the observed martensite microtextures at all stress/strain levels under uniaxial tensile deformation of metastable austenite under low temperature at a slow strain rate. The present investigation also proves that the Patel and Cohen’s classical theory can be utilized to predict the crystallographic variant selection, if it is correctly used along with the phenomenological theory of martensite crystallography.

On the relation between orientation relationships predicted by the phenomenological theory and internal twins in plate martensite

The phenomenological theory of martensite crystallography predicts two equivalent solutions for a particular habit plane in the case of a Fe–Ni–C alloy. Those two solutions differ in the magnitude of the inhomogeneous shear and in the orientation relationship (OR) they hold with austenite. Only the OR associated to the low shear solution has been observed experimentally so far. In the present study, the orientation relationship associated to the high shear solution is assessed experimentally using TEM measurements.

Crystallographic variant selection of martensite during fatigue deformation

Metastable austenitic stainless steels are prone to form deformation-induced martensite under the influence of externally applied stress. Crystallographic variant selection during martensitic transformation of metastable austenite has been investigated thoroughly with respect to the interaction between the applied uniaxial cyclic stress and the resulting accumulated plastic strain during cyclic plastic deformation. The orientation of all the Kurdjomov–Sachs (K-S) variants has been evaluated extensively and compared with the measured orientation of martensite with their corresponding interaction energies by applying the elegant transformation texture model recently developed by Kundu and Bhadeshia. Encouraging correlation between model prediction and experimental data generation for martensite pole figures at many deformed austenite grains has been observed. It has been found that both the applied uniaxial cyclic stress and the accumulated plastic strain are having strong influence on crystallographic variant selection during cyclic plastic deformation. Patel and Cohen’s classical theory can be utilized to predict the crystallographic variant selection, if it is correctly used along with the phenomenological theory of martensite crystallography.

Teoría cristalográfica de la transformación martensítica

La transformación martensítica es uno de los temas más investigados en la ciencia de los materiales durante el siglo XX. Precisamente la segunda parte de ese siglo se destacó por el desarrollo de diversas teorías relacionadas con la cinética de la transformación de esta fase, los mecanismos de nucleación y la forma como se produce el cambio de la estructura cristalina. En este trabajo se realiza la descripción de los diferentes conceptos que definen la cristalografía de la transformación martensítica, centrándose en la construcción y aplicación de los modelos cristalográficos más destacados: el modelo de Bain; el modelo de Wechsler, Lieberman y Read; y el modelo de Bowles y Mackenzie. Este desarrollo será realizado con base en características particulares de la transformación martensítica como su carácter no difusional, el tipo de intercara entre la fase madre (austenita) y la fase producto (martensita), la formación de la subestructura de defectos y el cambio de forma; todas estas descritas por medio de ecuaciones matemáticas que buscan predecir cómo se dará la transformación, más que en explicar el movimiento real de los átomos dentro de la estructura. Este desarrollo es conocido como la Teoría Fenomenológica de la Cristalografía de la Martensita (TFCM).

Orientation dependence of the martensite transformation in a quenched and partitioned steel subjected to uniaxial tension

The orientation dependence of the austenite-to-martensite transformation during uniaxial tensile testing was modelled using the phenomenological theory of martensite crystallography and the mechanical driving force. It was validated experimentally by means of electron backscatter diffraction measurements on a pre-defined zone of a quenched and partitioned steel during interrupted tensile tests. A close match is obtained between the predictions of the model and the experimental observations.

Pattern formation during cubic to orthorhombic martensitic transformations in shape memory alloys

The superelasticity and shape memory effect of shape memory alloys originate from martensitic transformations (MT) that produce self-accommodated polydomain structures. In order to understand the formation mechanism of various domain patterns, a phase field model of cubic to orthorhombic MT in NiTiPt and NiTiCu is formulated, through which microstructure evolutions dominated by long-range elastic interactions are simulated. A rich variety of morphological patterns are predicted and analyzed. In particular, autocatalytic events leading to multi-variant “pyramidal triangular” and “nested triangular” configurations in NiTiCu are revealed. These morphological patterns are beyond the reach of the classical phenomenological theory of martensitic crystallography (PTMC). The simulation predictions agree well with experimental observations. By distinguishing deformation variant from orientation variant, the theoretical connection and distinction between PTMC and phase field microelasticity theory are discussed, and their predictions are compared with experimental observations.

Non-classical {3 3 4}β type of twinned α′ martensite in a Ti–5.26 wt.% Cr alloy

Some uncommon crystallographic features of α′ martensite were characterized in the martensitic transformation in a water-quenched Ti–5.26wt.% Cr alloy. A pair of martensite plates, type K and type M, sit side-by-side and share a {334}β habit plane. However, they have different habit planes in terms of the hexagonal close-packed lattice. While the classical phenomenological theory of martensite crystallography (PTMC) is unable to explain the habit plane of type K martensite even though they contain {11¯01¯} internal twins, application of the edge-to-edge matching (E2EM) model succeeded in accounting for both the orientation relationship and the habit plane orientation of the two types of martensite. The elastic strain energy as a function of the thickness of type K martensite plates was calculated, and the result supports the preference of the E2EM model over PTMC in explaining this type of martensite. In addition, a self-accommodation mechanism for strain was proposed to maintain the macroscopic invariant plane, and reduce the overall elastic strain energy of the adjacent pair of martensite plates. The application of the E2EM model plus this self-accommodation mechanism provides a new perspective on understanding martensitic transformations and providing a link between the crystallography of displacive and diffusional transformations.

Transformation Mechanism of Preprecipitation NiMn Nanostructures

The transformation mechanism of constrained b.c.c NiMn (β phase) clusters coherently precipitated during isothermal aging of Fe-Ni-Mn maraging alloy at 753 K (480 °C) has been studied. Preprecipitation of β-NiMn phase was demonstrated using conventional and high-resolution transmission electron microscopy and confirmed by flanking of electron diffraction spots, X-ray diffraction sidebands, and the invariance of lattice parameter and peak breadths in the earlier stages of age hardening. The β-NiMn clusters were recognized with interfacial dislocation dipoles lying on {011}α planes and Burgers vectors of a0\( \left\langle {01\overline{1} } \right\rangle_{\alpha } \) type. During further aging, the β-NiMn clusters transformed martensitically into fct NiMn (θ phase) precipitates as envisaged by the characteristic microtwinning texture. Considering the anomalous elastic softness of β-NiMn alloy, the transformation was plausibly assumed to take place by the localized soft-mode mechanism in which the structural instability of clusters is stimulated by the strain field of the interfacial dislocations. Computerized calculations in accordance with the phenomenological theory of martensite crystallography indicated that microtwinning of martensitic θ precipitates occurs in a self-accommodating manner. Transformation of very small β clusters at earlier stages of aging is thermodynamically hampered by the interfacial energy barrier.

冷延焼鈍後のフェライト−マルテンサイト二相組織鋼中のマルテンサイトの結晶学的組織解析

Cold-rolled and annealed ferrite-martensite dual phase (DP) steel sheets are a useful material for automotive applications because of their excellent balance of strength and ductility. Although few research papers have examined the crystallography and microstructure of lath martensite in DP steel, the characteristics of lath martensite have been investigated in single-phase martensitic steel. In the present study, the crystallography and microstructure of lath martensite in a ferrite-martensite dual phase were studied using electron microscopy and electron diffraction analysis, and the crystallographic orientation relationship between the ferrite and martensite was analyzed. The main results are as follows: (1) The lath martensite in DP steel consists of some number of packets, and these packets consist of blocks. This structure is the same as the microstructure of single-phase lath martensite. (2) The habit planes of the martensite laths in a packet tend to be parallel to the close-packed plane of the adjacent ferrite grain, whose fraction is about 30%.

Deformation twinning in Ni2MnGa

Deformation twinning is investigated in the martensitic phase of a Ni46.75Mn34Ga19.25 (at.%) alloy. X-ray and electron diffraction are used to establish the crystallography of the non-modulated tetragonal martensite, and transmission electron microscopy is employed to deduce the twinning parameters. It is convenient to define the twinning parameters with respect to a “monoclinic” unit cell, designated 2M: then K1, η1, K2, and η2 are (001), [100], (100), and [001] respectively. The Burgers vector of the active twinning disconnections is close to 1/6[100] and the disconnections are associated with steps of height d(002). These defects are expected to be highly mobile since their motion does not require atomic shuffling. It is shown that periodic arrangements of two layer twins produce modulated crystal structures, such as 14M.

Connectivity of slip systems between different phases in ferrite–martensite dual-phase steels

► The crystallographic study of ferrite and martensite in dual-phase was performed. ► Crystal orientation relationship was examined between martensite and ferrite. ► The parallel relationship depends on the heat-treatments of the specimens. ► They suggest the formation of martensite laths. Ferrite–martensite dual-phase high-strength steels exhibit good formability. This study focuses on the morphology and crystallography of martensite and ferrite in these steels by using quantitative analysis. Three kinds of ferrite–martensite dual-phase specimens subjected to three different heat treatments, step-quenched, hot-rolled–annealed–quenched and quenched–annealed–quenched, were used as specimens in the experiments. Martensite in hot-rolled–annealed–quenched specimens exhibits a parallel relationship between the common close-packed planes of martensite packets and the close-packed planes of adjacent ferrites. This is because these specimens contain fine film-like austenite regions. Fine grained austenite contains high elastic strain energy. Martensite laths, whose shear directions are parallel to their habit planes, are formed from fine austenite regions to accommodate martensitic transformation strain induced by emitting dislocations into adjacent ferrite grains.

Characterization of 3R martensite in a Ni–40Al–15Pt bulk alloy

As Pt promotes the reversible martensite transformation, the aim of this study was to assess the influence of Pt on the crystallography of (β′) martensite, in terms of ordering adapted, twinning and stacking faults. The focused ion beam (FIB) milling process was used to prepare transmission electron microscopy (TEM) samples of the NiAlPt bulk alloys, whereby 3R, L10 ordering of the martensite was confirmed. The addition of Pt, coupled with high temperature oxidation resulted in more stacking faults, due to greater Pt diffusion and subsequent enrichment in martensite. For Pt diffusion the temperature must be in excess of 900°C, both for isothermal and cyclic oxidation. When the favorable temperature environment is achieved Pt can diffuse preferentially allowing for promotion of the transformation to martensite.

Quantitative Analysis of Variant Selection for Displacive Transformations Under Stress

The existing variant selection models for displacive transformations are mostly qualitative in nature and attempt to predict the bulk texture using several fitting parameters. Many of these models use Kurdjumov-Sach (K-S) type orientation relationships (ORs) and ignore the phenomenological theory of martensite crystallography. So far there has not been any attempt to assess variant selection in the level of individual variants within one austenite grain. In this work, new kinds of experiments and innovative mathematical models have been developed to critically assess the variant selection phenomenon during bainite transformation under externally applied stress. Volume fractions of individual variants in a austenite grain have been calculated for the first time. Patel and Cohen’s theory on variant selection has been used in a new mathematical framework. Hitherto unknown aspects of variant selection have been found, which is exciting and provides new insight into the subject.

Application of the O-line model to martensite crystallography

The O-line model is usually applied to precipitation crystallography. Its application to investigation of martensite crystallography has received little attention. In this paper, the relationship between O-line model and the prism matching model for martensite crystallography is established. The formulas in the O-line model are applicable to martensite crystallography. Analytical solution of the habit plane corresponding to the minimum shape strain has been derived. A calculation example of {3 10 15}f martensite in a ferrous alloy is provided. While the results are in agreement with the former models for martensite crystallography, the advantage of O-line model is that it offers analytical solutions, facilitating further systematic investigations.

Investigation on martensitic steel using a quenching-partitioning-tempering process via electron backscatter diffraction analysis

A new quenching-partitioning-tempering (Q-P-T) process was designed based on the recently developed quenching and partitioning (Q & P) treatment by Speer et al. The orientation relationships (ORs) of martensite (α) in Q-P-T steel tempered under different conditions were investigated using a scanning electron microscope with an electron backscatter diffraction unit. The morphology and crystallography of lath martensite within a packet were analyzed. Martensites exhibiting an initial austenite (γ) grain in the orientation image map of different samples were chosen and their {111}α pole figures were drawn. The pole figures were fitted according to the ideal Kurdjumov-Sachs (K-S) and Nishiyama-Wasserman (N-W) ORs, which were calculated using Matlab and with a γ crystal-oriented (001)γ[100]γ as the reference frame. The martensite OR in the Q-P-T steel follows both the K-S and N-W ORs; however, the K-S OR is predominant. This characteristic does not change in the samples further tempered at different temperatures.

Crystallographic Analysis of Martensite in 0.2C-2.0Mn-1.5Si-0.6Cr Steel using EBSD

The crystallography of martensite formed in 0.2C-2.0Mn-1.5Si-0.6Cr steel was studied using the electron backscattered diffraction (EBSD) technique. The results showed that the observed orientation relationship (OR) was closer to that of Nishiyama-Wassermann (N-W) than Kurdjumov-Sachs. The martensite consisted of parallel laths forming morphological packets. Typically, there were three different lath orientations in a morphological packet consisting of three specific N-W OR variants sharing the same {111} austenite plane. A packet of martensite laths with a common {111} austenite plane was termed a crystallographic packet. Generally, the crystallographic packet size corresponded to the morphological packet size, but occasionally the morphological packet was found to consist of two or more crystallographic packets. Therefore, the crystallographic packet size appeared to be finer than the morphological packet size. The relative orientation between the variants in crystallographic packets was found to be near 60°/ , which explains the strong peak observed near 60° in the grain boundary misorientation distribution. Martensite also contained a high fraction of boundaries with a misorientation in the range 2.5-8°. Typically these boundaries were found to be located inside the martensite laths forming sub-laths. © 2011 The Chinese Society for Metals.

A phase-field model for incoherent martensitic transformations including plastic accommodation processes in the austenite

If alloys undergo an incoherent martensitic transformation, then plastic accommodation and relaxation accompany the transformation. To capture these mechanisms we develop an improved 3D microelastic–plastic phase-field model. It is based on the classical concepts of phase-field modeling of microelastic problems (Chen, L.Q., Wang Y., Khachaturyan, A.G., 1992. Philos. Mag. Lett. 65, 15–23). In addition to these it takes into account the incoherent formation of accommodation dislocations in the austenitic matrix, as well as their inheritance into the martensitic plates based on the crystallography of the martensitic transformation. We apply this new phase-field approach to the butterfly-type martensitic transformation in a Fe–30 wt%Ni alloy in direct comparison to recent experimental data (Sato, H., Zaefferer, S., 2009. Acta Mater. 57, 1931–1937). It is shown that the therein proposed mechanisms of plastic accommodation during the transformation can indeed explain the experimentally observed morphology of the martensitic plates as well as the orientation between martensitic plates and the austenitic matrix. The developed phase-field model constitutes a general simulations approach for different kinds of phase transformation phenomena that inherently include dislocation based accommodation processes. The approach does not only predict the final equilibrium topology, misfit, size, crystallography, and aspect ratio of martensite–austenite ensembles resulting from a transformation, but it also resolves the associated dislocation dynamics and the distribution, and the size of the crystals itself.